Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
- Integral of sqrt(xy-y^2)
- Integral of sin(npix/l)
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Integral of 5sqrt(8-3x)^6
- Integral of (1-cos2wt)
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Identical expressions
- sin(npix/l)
- sinus of (n Pi x divide by l)
- sinnpix/l
- sin(npix divide by l)
- sin(npix/l)dx
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Similar expressions
- sin(n*pi*x)/l
Integral of sin(npix/l) dx
The solution
You have entered
[src]
1 / | | /n*pi*x\ | sin|------| dx | \ l / | / 0
$$\int\limits_{0}^{1} \sin{\left(\frac{\pi n x}{l} \right)}\, dx$$
The answer (Indefinite)
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/ // /pi*n*x\ \ | ||-l*cos|------| | | /n*pi*x\ || \ l / | | sin|------| dx = C + |<--------------- for n != 0| | \ l / || pi*n | | || | / \\ 0 otherwise /
$$-{{l\,\cos \left({{n\,\pi\,x}\over{l}}\right)}\over{n\,\pi}}$$
The answer
[src]
/ /pi*n\ | l*cos|----| | l \ l / pi*n <---- - ----------- for ---- != 0 |pi*n pi*n l | \ 0 otherwise
$${{l}\over{n\,\pi}}-{{l\,\cos \left({{n\,\pi}\over{l}}\right)}\over{
n\,\pi}}$$
=
=
/ /pi*n\ | l*cos|----| | l \ l / pi*n <---- - ----------- for ---- != 0 |pi*n pi*n l | \ 0 otherwise
$$\begin{cases} - \frac{l \cos{\left(\frac{\pi n}{l} \right)}}{\pi n} + \frac{l}{\pi n} & \text{for}\: \frac{\pi n}{l} \neq 0 \\0 & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.